Finite Group Databasebeta

← #14660480

Subgroups — #14660480

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622849C212yesmaximal
2C2×#10622838C212yesmaximal, complemented
3#13068355C211yesmaximal, characteristic, complemented
4#13068349C211yesmaximal, characteristic, complemented
5C2×C11×#536C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C23×Q8×C11C2211yescharacteristic
8C11×#536—24no—
9C11×#536—24no—
10C2×C11×C4⋊Q8C412yescomplemented
11C2×C11×#124C412yescomplemented
12C2×C11×#123—22no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2212yes—
16C22×#4318C2212yes—
17#10622849—24no—
18#10622849—24no—
19C2×#66901—24no—
20#10622838—24no—
21#10622838—24no—
22C2×#66899—24no—
23#10622168—22no—
24#10622164—22no—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41D414yes—
31C22×Q8×C11—21no—
32C22×Q8×C11—22no—
33C22×Q8×C11—22no—
34C22×Q8×C11—22no—
35C22×Q8×C11—22no—
36C22×Q8×C11—22no—
37C22×Q8×C11C2×C412yes—
38C22×Q8×C11C2×C411yescharacteristic
39C22×Q8×C11D414yes—
40C22×D4×C11—21no—
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C11×C4⋊Q8—24no—
46C11×C4⋊Q8—24no—
47C11×#124—24no—
48C11×#124—24no—
49C11×#123—216no—
50C11×C22⋊Q8—216no—
51C11×#117—22no—
52C11×#117—22no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4D412yes—
57C2×C42×C11C2×C412yes—
58C2×C22⋊Dic11—22no—
59#66979—22no—
60#66979—22no—
61#66979—22no—
62#66979D414yes—
63C2×C4⋊Dic11—22no—
64C2×C4×Dic11—22no—
65C2×#4318—22no—
66C2×#4318—22no—
67C2×#4318—22no—
68C2×#4318—22no—
69C2×#4318—22no—
70C2×#4318D414yes—
71C22×C11⋊C8—22no—
72#66901—216no—
73#66899—216no—
74#11007—111nomaximal, Sylow
75C24×C11—21no—
76C24×C11C2×D411yescharacteristic
77C11×#41—24no—
78C11×#41—24no—
79C11×#41—24no—
80C11×#41—24no—
81C11×#41—42no—
82C11×#41—42no—
83C11×#41—42no—
84C11×#41—42no—
85C2×Q8×C11—22no—
86C2×Q8×C11—21no—
87C2×Q8×C11—24no—
88C2×Q8×C11—24no—
89C2×Q8×C11—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—24no—
93C2×Q8×C11—24no—
94C2×Q8×C11—24no—
95C2×Q8×C11—24no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×Q8×C11—41no—
102C2×Q8×C11—41no—
103C2×Q8×C11C22⋊C414yes—
104C2×Q8×C11C22⋊C412yes—
105C2×D4×C11—24no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—42no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11C22⋊C412yes—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—42no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11—42no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11C22⋊C414yes—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×Dic11—42no—
133C11×C4⋊C4—216no—
134C11×C4⋊C4—24no—
135C11×C22⋊C4—216no—
136C11×C22⋊C4—24no—
137C42×C11—22no—
138C42×C11—22no—
139C22⋊Dic11—24no—
140C22⋊Dic11—42no—
141C4⋊Dic11—24no—
142C4⋊Dic11—42no—
143C4×Dic11—24no—
144C4×Dic11—42no—
145#4318—24no—
146#4318—24no—
147#4318—42no—
148#4318—42no—
149C2×C11⋊C8—24no—
150C2×C11⋊C8—42no—
151C2×C11⋊C8—42no—
152C2×#536D1111yescharacteristic
153C2×#421—112no—
154C2×#419—112no—
155#1742—111no—
156#1740—111no—
157C23×C11—22no—
158C23×C11—42no—
159C23×C11—44no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C2×C22⋊C411yescharacteristic
163C23×C11#12012yes—
164C23×C11#12112yes—
165C23×C11#12411yescharacteristic
166C23×C11#12711yescharacteristic
167Q8×C11—28no—
168Q8×C11—24no—
169Q8×C11—44no—
170Q8×C11—42no—
171Q8×C11—44no—
172Q8×C11—44no—
173D4×C11—24no—
174D4×C11—44no—
175D4×C11—44no—
176D4×C11—42no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—44no—
185C2×C4×C11—44no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11—44no—
189C2×C4×C11C2×C22⋊C411yescharacteristic
190C2×C4×C11C2×C22⋊C411yescharacteristic
191C2×C4×C11C4×D412yes—
192C2×C4×C11C4×D412yes—
193C2×C4×C11#12012yes—
194C2×C4×C11#12012yes—
195C2×C4×C11#12012yes—
196C2×C4×C11#12112yes—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11#12312yes—
202C2×C4×C11#12312yes—
203C2×C4×C11#12411yescharacteristic
204C2×C4×C11#12711yescharacteristic
205C2×Dic11—44no—
206C2×Dic11—84no—
207C11⋊C8—44no—
208C22×#41C2×D1111yescharacteristic
209C23×Q8C2×D1111yescharacteristic
210C22×M16—112no—
211#536—24no—
212#536—24no—
213C2×C4⋊Q8Dic1112yescomplemented
214C2×#124Dic1112yescomplemented
215C2×#123—22no—
216C2×C22⋊Q8—22no—
217C2×#117—112no—
218C2×#117C2×D1111yescharacteristic
219#421—224no—
220#421—224no—
221C2×#104—224no—
222#419—224no—
223#419—224no—
224C2×#103—224no—
225#343—222no—
226#342—222no—
227C22×C11—22no—
228C22×C11—24no—
229C22×C11—42no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—44no—
233C22×C11—42no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11#37911yescharacteristic
237C22×C11#39011yescharacteristic
238C22×C11#39011yescharacteristic
239C22×C11#39212yes—
240C22×C11#39412yes—
241C4×C11—44no—
242C4×C11—42no—
243C4×C11—44no—
244C4×C11#38612yes—
245C4×C11#38612yes—
246C4×C11#39212yes—
247C4×C11#39412yes—
248Dic11—84no—
249C2×#41—22no—
250C2×#41—22no—
251C2×#41—22no—
252C2×#41—22no—
253C2×#41—22no—
254C2×#41C22⋊D1114yes—
255C22×Q8—21no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8C2×Dic1112yes—
262C22×Q8C2×Dic1111yescharacteristic
263C22×Q8C22⋊D1114yes—
264C22×D4—21no—
265C22×D4C2×Dic1111yescharacteristic
266C23×C4—21no—
267C23×C4—21no—
268C23×C4C22×D1111yescharacteristic
269C2×M16—114no—
270C2×M16—222no—
271C2×M16—222no—
272C2×M16—222no—
273C2×M16—222no—
274C2×M16—222no—
275C22×C8—222no—
276C4⋊Q8—24no—
277C4⋊Q8—24no—
278#124—24no—
279#124—24no—
280#123—216no—
281C22⋊Q8—216no—
282#117—22no—
283#117—22no—
284#117—114no—
285#117—222no—
286#117—222no—
287#117—222no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4C22⋊D1112yes—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4C22⋊D1112yes—
294C2×C42—222no—
295C2×C42C2×Dic1112yes—
296#104—2216no—
297#103—2216no—
298C2×C11—22no—
299C2×C11—21no—
300C2×C11—21no—
301C2×C11—22no—
302C2×C11—82no—
303C2×C11#143811yescharacteristic
304C2×C11#179612yes—
305C24—21no—
306C24C2×C22⋊D1111yescharacteristic
307#41—24no—
308#41—24no—
309#41—24no—
310#41—24no—
311#41—42no—
312#41—42no—
313#41—42no—
314#41—42no—
315C2×Q8—22no—
316C2×Q8—21no—
317C2×Q8—24no—
318C2×Q8—24no—
319C2×Q8—24no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—24no—
323C2×Q8—24no—
324C2×Q8—24no—
325C2×Q8—24no—
326C2×Q8—42no—
327C2×Q8—41no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×Q8—42no—
332C2×Q8—41no—
333C2×Q8C22⋊Dic1114yes—
334C2×Q8C22⋊Dic1112yes—
335C2×D4—24no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—21no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4C22⋊Dic1112yes—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—41no—
348C22×C4—42no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—42no—
352C22×C4—41no—
353C22×C4—442no—
354C22×C4C22⋊Dic1114yes—
355C22×C4D4×D1112yes—
356C22×C4D4×D1112yes—
357C22×C4#434112yes—
358C22×C4#434112yes—
359C22×C4C22×Dic1111yescharacteristic
360C22×C4C2×C22⋊D1112yes—
361C22×C4C2×C22⋊D1112yes—
362C22×C4C2×C22⋊D1111yescharacteristic
363M16—224no—
364M16—224no—
365M16—442no—
366M16—442no—
367C2×C8—224no—
368C2×C8—442no—
369C2×C8—442no—
370C4⋊C4—216no—
371C4⋊C4—24no—
372C4⋊C4—224no—
373C4⋊C4—442no—
374C22⋊C4—216no—
375C22⋊C4—24no—
376C22⋊C4—224no—
377C22⋊C4—442no—
378C42—22no—
379C42—22no—
380C42—224no—
381C42—442no—
382C11#1100711yescharacteristic, complemented, Sylow
383C23—22no—
384C23—42no—
385C23—44no—
386C23—41no—
387C23—41no—
388C23#6698911yescharacteristic
389C23#6699112yes—
390C23#6699311yescharacteristic
391C23C2×C22⋊Dic1111yescharacteristic
392C23#6700612yes—
393Q8—28no—
394Q8—24no—
395Q8—44no—
396Q8—42no—
397Q8—44no—
398Q8—44no—
399D4—24no—
400D4—44no—
401D4—44no—
402D4—42no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—444no—
416C2×C4—884no—
417C2×C4D4×Dic1112yes—
418C2×C4D4×Dic1112yes—
419C2×C4#6698812yes—
420C2×C4#6698812yes—
421C2×C4#6698911yescharacteristic
422C2×C4#6699012yes—
423C2×C4#6699012yes—
424C2×C4#6699112yes—
425C2×C4#6699212yes—
426C2×C4#6699212yes—
427C2×C4#6699212yes—
428C2×C4#6699212yes—
429C2×C4#6699311yescharacteristic
430C2×C4C2×C22⋊Dic1111yescharacteristic
431C2×C4C2×C22⋊Dic1111yescharacteristic
432C2×C4#6700612yes—
433C8—444no—
434C22—22no—
435C22—24no—
436C22—41no—
437C22—42no—
438C22—41no—
439C22—44no—
440C22—42no—
441C22—82no—
442C22—82no—
443C22#1062283411yescharacteristic
444C22#1062283411yescharacteristic
445C22#1062283512yes—
446C22#1062283612yes—
447C22#1062286011yescharacteristic
448C4—44no—
449C4—42no—
450C4—44no—
451C4—884no—
452C4#1062283312yes—
453C4#1062283312yes—
454C4#1062283512yes—
455C4#1062283612yes—
456C2—22no—
457C2—21no—
458C2—21no—
459C2—22no—
460C2—82no—
461C2#1306685711yescharacteristic
462C2#1306859112yes—
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#536C2
socleC22×C11#379
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC2×#536D11
hypocenterC11#11007
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#536

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622838C2semidirect
3. #13068355C2semidirect
4. #13068349C2semidirect
10. C2×C11×C4⋊Q8C4semidirect
11. C2×C11×#124C4semidirect
213. C2×C4⋊Q8Dic11semidirect
214. C2×#124Dic11semidirect
382. C11#11007semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106228492
C2×#106228382
#130683552
#130683492
C2×C11×#5362
#1100711